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Objectives of this Chapter, one should be able to:
  1. Identify terms, Like terms and unlike terms.  
  2. Combing Like terms. 
  3. Using the Distributive Property to remove parentheses.  
  4. Write simple word phrases as algebraic expressions. 

Before we practice simplifying expressions, some new languare of algebra must be presented. A term is a number of the product of anuber and a variable raised to some power (in most cases). Additionally, the numerical coefficient of a term is the numberical factor. For example, the numberical coefficient of (3x) is the 3. Recall that 3x really mens 3 times x.

Term Numerical Coefficient

sometimes just called the coefficient













Terms with the same variable raised to exactly the same power are called Like Terms. In like manner terms that aren't like terms are called Unlike Terms.
Like Terms Unlike Terms
3x, 2x

-6 x2y, 2x2y, +4x2y,

-2 abc, +3 abc, -.025 abc

5x, 5x3

7y, 3z, 8x2

+6abc, -6a2b3

In like terms, each variable and its exponent must match exactly, but these fractors do not have to be in the same order. For example 2x2y and 3yx2 are like terms.
Simplifying expressions makes frequent use of the distributive property to remove parentheses.

If a " minus" sign precedes parentheses,then sign of each term inside the parentheses is changed when the distributive property is applied to remove the parenthesis itself.


-(2x +1) =

-2x -1

-(-5x +y -z ) =

+5x -y +z

-(+x-2y) =

-x +2y

-(-3x-4y-1) =

+3x +4y + 1

Example 1. Remove the parentheses and combine and simplify like terms of the

following expression: 8 -(7x +2 ) +3x - 2(4x +7) - (3x- 1) ?

First remove the parentheses 8 -(7x +2 ) +3x - 2(4x +7) - (3x- 1 =

+8 -7x -2 +3x -8x -14 -3x +1

Now we need to combine like terms +8 -2 -14 +1 = -7

-7x +3x -8x -3x = -15x

Now write the variable first then the numberical coefficient

for the final simplification of the expression

-15x -7